Linear or arcuate hydraulic pump or motor

ABSTRACT

A hydraulic pump or motor having ball pistons, working in cylinders side-by-side in a linear or arcuate array, and engaging an extended linear or arcuate cam track.

United States Patent inventors Donald Firth;

Sinclair Upton Cunningham, both of East Kilbride, Glasgow, Scotland Applr No. 850.342

Filed Aug. 13, 1969 Patented Sept. 7, 1971 Assignee National Research Development Corporation London, England Continuation of application Ser. No. 644,989, June 9, 1967, now abandoned.

LINEAR OR ARCUATE HYDRAULIC PUMP OR MOTOR 10 Claims, 9 Drawing Figs.

US. Cl 91/501, 91/180 Int. Cl F011 33/02, F04b 1/02 Field of Search 103/161,

161A,161V,162,162P;91/199,202,180

[56] References Cited UNITED STATES PATENTS 2,101,829 12/1937 Beneder 91/498 2,617,360 11/1952 Barker 103/162 2,712,794 7/1955 Humphreys .1 103/161 2,882,831 4/1959 Dannevig 103/161 3,046,950 7/1962 Smith 103/124 3,151,529 10/1964 Leath 91/491 3,287,993 11/1966 Lomnicki 74/567 FOREIGN PATENTS 906,553 9/1962 Great Britain Primary ExaminerWil1iam L. F reeh Attorney-Larson, Taylor & Hinds ABSTRACT: A hydraulic pump or motor having ball pistons, working in cylinders side-by-side in a linear or arcuate array, and engaging an extended linear or arcuate cam track.

PATENTED SEP 7197! SHEET 2 OF 6 PATENTEBSEP Yum 3503211 SHEET 3 BF 6 PATENTEDSEP nan SHEET BF 6 PATENTED SEP 7 l9?! sum 5 or 6 LINEAR ORARCUATE HYDRAULIC PUMP OR MOTOR This application is a continuation application of application Ser. No 644,989 filed June 9, [967, now abandoned.

iTheshape and pitch of the cam lobes. in relation to the number and pitch of the cylinders, is chosen so that the acceleration of eachpiston at the start of each'ofits strokes is coincident with a conjugate deceleration of another piston at the end of a stroke in the same direction, and vice versa, such acceleration and deceleration of each piston being separated by a constant velocity phase occupying a proportion of the stroke determined by a formula the value of which is zero for certain combinations of piston number and lobe pitch.

The cam profiles may provide a dwell at the beginning and end of each stroke of a piston and each such dwell on the part of one piston coincides with a period of constant velocity in the stroke in the same direction, of another piston.

Sharp transitions of the velocity characteristics of the pistons may be rounded off" by modification of the cam profiles, to avoid high Hertzian stresses where the ball pistons traverse the crests of the cam lobes but the velocity charac' teristics must be symmetrical about the modstroke position to preserve the said conjugasy between coincident accelerations of one piston and decelerations of another.

The structure described has pairs of ball pistons in coaxial outwardly facing cylinders, and duplicate cam tracks on either side of the cylinder block, to balance out yawing couples which would exist between the cylinder block and a single cam track.

For added hydraulic stiffness the inner cylinder ends may be part spherical to match the ball pistons, so reducing the cylinder dead space at inner dead center.

A rotary distributor valve, as near to the cylinders as possible controls fluid flow to and from the cylinders and is driven by engagement of a pinion with a rack running alongside the cam track.

This invention relates to hydraulic machines, which expression includes pumps and motors, having two parts relatively movable in a linear or arcuate manner, one of the parts having a series of cylinders with piston members therein, and the other part having a cam track with a series of half-lobes engageable by the piston members, and valve means operable to supply fluid to and release fluid from the cylinders in accordance with the relative positions of the parts. Examples are described in UK. Pat. specification Nos. 924,906 and 961,339.

With such pumps and motors, the relation between the force the fluid flow from the pump or the force produced by the motor are usually not independent of the relative positions of the parts, other conditions being constant. This is a disadvantage in some cases, for example where a rnotoris used as a servomotor to accurately position an object.

It is therefore an object ofthis invention to provide a linear or arcuate hydraulic pump or motor having fluid flow or force output which is independent of the relative positions of the parts, other conditions being constant.

According to the present invention, a hydraulic machine includes two parts which are relatively movable along an armate path of radius up to and including infinity, that is to say including a linear path, one of the parts having a series of cylinders with piston members therein, and the other part having a cam track, aligned along the said path and engageable by the piston members, the cylinders and pistons being arrayed side by side along the direction of the cam track and valve means operable to supply fluid to and release fluid from the cylinders in accordance with the relative positions of the parts, the cam track having a series of similarly contoured half-lobes each having a profile which causes a piston member moving thereover, during a half-cycle of its reciprocation in its cylinder, to have three consecutive phases of motion, namely an acceleration phase, a succeeding constant velocity phase and a final deceleration phase, and the variations in the velocity of movement of each piston member in its cylinder tions resultant from movement of'anotherpiston member in its cylinder over the appropriate sections of a half-lobe of the cam track, the constant velocity phase occupying not less than a proportion of the said half-cycle according to the expression l(2L/n) where n/L is an odd number and according to the expression l(4L/n) when n/L is an even number, n being the number of cylinders and L being the highest common factor of n and m, where m is the number of lobes of the cam track spanned by a distance along the said path equal to n times the distance between the axes of adjacentcylinders, including the case where the value of the expression l-(4L/r'i) is zero.

Preferably the acceleration and deceleration of each piston element during the said acceleration and deceleration phases, is constant as in this way the peak acceleration imposed on a piston element is at a minimum but the requirement aforesaid of constant fluid flow for a pump or constant force from a motor, is met if the acceleration of a piston element during its acceleration phase and the balancing deceleration of another piston element are conjugate in the sense that the sum of the velocities of the two piston elements is constant.

Each piston member presents to the cam track a profile which is at least part of a circle, viewed in the plane of the cam track.

Each piston member may consist of a spherical ball or may comprise a spherical ball or part spherical element at the end which engages the cam track.

Alternatively each piston member may have a cylindrical roller mounted in the end which engages the cam track.

For the sake ofsimplicity eachpiston member is hereafter referred to as a ball" and it is to be understood that this term includes a piston not-itself a ball but which comprises a part circle, spherical ball,.part spherical element or roller as explained in the three immediatelypreceding' paragraphs.

Each half-lobe profile may be so shaped that the path followed by the center of the said circle, ball, part spherical ele* ment or roller during the three consecutive phases of motion is defined by the following three equations:

Constant acceleration phase:

x is the distance of the center of the ball along the cam:

track, from the bottom dead center of the first lobe P, is the cam lobe pitch distance r is the distance of the center of the ball from its bottom dead center position,

r is the stroke of the ball.

These equations apply, to the case where eitherm or n is an odd integer and m and nhave no common factor greater than unity-or to the case where m and n are even integers, m/Z

and 11/2 have no common factor greaterthan unity, and n/2 is greater than three.

ders at any moment spans a section of the cani track which is repeated identically along the full length of the track arid it is mathematically convenient to regard this section as a cycle which is repeated along the track and to treatdistances from the start of the cycle as phase angles within this cycle and to w It will be appreciated that the assembly of pistons aridcylinexpress them in radians and/or degrees.

The length of these sections is equal to the number of balls multiplied by theinterball pitch distance P,. It is also equal to the number of lobes multiplied by the interlobe pitch distance P,, that is to say:

n P,,=m P and a radian represents a measurement along the cam track equal to the length of one of the said sections divided by 21;, that is to say: a

one radian n PJZvr m P,/21r

if. on the other hand, m=6 and n=9, that is to say n is odd and m and n have a common factor greater than one, the equations will be:

Constant acceleration phase:

1 1 Constant velocity phase:

1' 1 3 1 o n for 0 Constant deceleration phase:

lira/{is odd, where L is the highest common factor of m and n, then the minimum proportion of the stroke of each piston member occupied by the period of constant velocity is (1-(2 L/n). ll n/L is even, then the expression is l-(4L/n). These minimum" proportions of the stroke occupied by the constant velocity phase may only be exceeded when a dwell is provided as described in the two immediately succeeding paragraphs.

In the case where n/L is even there are certain values of m and rt for which the expression (l-(4L/n) is equal to zero so that the constant velocity phase is likewise reduced to zero and the constant deceleration phase follows directly upon the constant acceleration phase except where a dwell is provided as hereinafter explained. The zero constant velocity case is within the scope of the invention.

The cam profile may be so shaped that each piston member dwells at zero velocity at its innermost position in the cylinder and/or at its outermost position in the cylinder. This enables the valve means to be made with rather more tolerance in commencing the supply of fluid to a cylinder or releasing fluid from a cylinder than would be the case if there were no dwell.

As these dwells, at the inner and outer dead centers of the ball stroke, represent periods of no motion of the ball in question axial of its cylinder bore, it is necessary that they should each coincide in time with the constant velocity phase of another ball. This necessitates adding to the constant velocity phase of each ball; an amount equal to the length of these dwells. Furthermore, as a deceleration phase of one ball must exactly match the acceleration phase of another ball, the velocity diagram of ball motion must be kept symmetrical about the midstroke point so that the sequence becomesinncr dead center dwell-constant acceleration at higher rate than would be the case without dwellconstant velocity beginning earlier by the amount of the inner dead center dwell and ending later by the amount of the outer dead center dwell-constant deceleration at higher rate, i.e. beginning later and finishing earlier-outer dead center dwell. By this symmetrical velocity characteristic the aforesaid requirement of constant flow or force can be met where dwell is inserted.

lt is possible for a dwell on the part of one ball to be coincident with, and be matched by the coincident acceleration and deceleration phases of two other balls which together make a contribution equal to that of one other ball during its constant velocity phase but where this is done the constant flow or force requirement is not met unless the dwell is of the same duration as these acceleration and deceleration phases of the two other balls. This arrangement is not within the scope of the invention. 7

It should be noted that a sequence of dwell-acceleration constant velocity-decelerationdwell, must be followed by an exact replica of the sequence, for the return stroke of. the ball, and the velocity diagram of this stroke must be the mirror image of that of the working stroke, if the machine is to be reversible without change of performance. It follows therefore that the actual cam shape provides two dwell periods in succession a double length dwell period in fact) at each dead center position, one belonging to the inward stroke and one belonging to the outward stroke.

For the case where dwell is provided, the equations quoted above for the case where m=6 and n=9 would be modified as follows:

Constant acceleration phase:

H l im-m) where 8 is half of the total extent of the dwell in radians as hereinbefore defined.

It should be emphasized that any convenient dimension can be chosen for the dwell so long as the above modifications. are made to the active strokes of the balls.

The cam profile may be modified in such a manner that the period of constant acceleration begins and finishes with a nonabrupt transition from the preceding and to the succeeding period, that is to say a graph of velocity of a piston member against distance travelled along the cam track would show a rounded elbow to the curve at the beginning and end of the constant acceleration line rather than having an abrupt change of slope. The cam profile must then be similarly modified to produce a similar transition at the beginning and end of a period of deceleration, if the acceleration phase of one piston element is to be conjugate with the balancing deceleration of another piston clement. Such a transition is especially beneficial as a piston member reaches and leaves its innermost position in its cylinder, that is to say as the piston member passes over a crest of a lobe on the cam track, to mitigate the extreme convexity of profile liable to exist at this point, which can cause high Hertzian stresses.

Where each piston includes or consists of a ball, or includes a part spherical portion engaging the cam track, the cam track may have a groove, in which the ball or part spherical portion travels, at least at and approaching the crest of the lobe, the groove having a radius not less than that of the ball or part spherical portion and progressively deepening towards the crest from each side. Such a groove reduces Hertzian stresses on the piston member.

The invention is illustrated, merely by way of example, by certain preferred embodiments of the invention taking the form of a drive for use on a machine took, such embodiments being shown in the accompanying drawings in which:

FIG. 1 is a plan of part of an embodiment of the invention taken on the line 1-1 of FIG. 2, v

FIG. 2 is a part sectional and elevation of the structure shown in FIG. 1 taken on the line 22 of that Figure,

FIG. 3 is a part sectional side elevation of part of the apparatus shown in FIG. 2,

FIG. 4 is a diagrammatic view of part of the hydraulic system of the apparatus shown in FIGS. 1 to 3, and

FIG. 5 is a velocity diagram relating to this embodiment of the invention,

FIGS. 6, 6a and 6b are velocity diagrams relating to another embodiment of the invention and,

FIG. 7 is a diagrammatic drawing of parts of the said other embodiments.

These embodiments are intended for use in the case where the path of relative motion between the piston/cylinder assembly and the cam track is linear, which may be regarded as the case where such path follows an arc of infinite radius but it should be understood that the same principles apply to the case where the path follows an arc of finite radius which latter arrangement is within the scope of the invention.

In FIG. 1 there is shown a machine tool comprising a bed 10 and a table 11 which are relatively movable. Fixed to the bed 10 is a housing 12 the upper part of which is provided with eight aligned bores 13 each of which constitutes a cylinder. Spherical balls 7a-h and 80-h are mounted in the cylinders 13, two balls 7, 8 being disposed in each of the cylinders 13. Thus sixteen balls 7a-h are provided in the housing 12. The balls 7, 8 are slidably mounted within the cylinders 13 for axial movement therein.

An insert 14 is disposed centrally of the length of each of the cylinders 13, each insert 14 having oppositely facing hemispherical concave surfaces1i T6 onto which the balls 7:8 seat in their bottom dead center positions i.e. when they are closest to one another adjacent the center of the cylinder 13. The center of the insert 14 is apertured as at 17 such that opposite ends of each cylinder 13 communicate with one another. A duct 18 communicates with the interior of each cylinder 13, such that hydraulic fluid may be supplied through duct 18 to the interior of each cylinder 13 between balls 7 and 8 whereby these balls may be forced outwardly or drawn inwardly according to the pressure of the fluid within the cylinder. The hydraulic system for pumping hydraulic fluid into and out of the cylinders 13 via ducts 18 will be described hereinafter.

The table 11 is slidably mounted over the housing 12 and is provided along its length with an inverted channel 20 the sides of which provide cam faces 21, 22. Each of the cam faces 21, 22 comprises a plurality of substantially identical symmetrical ramps each of which is provided with oppositely inclined flanks. Thus the cam faces 21, 22 are of sinuous form but no attempt is made to reproduce accurately their correct profiles in FIG. 1. The balls 7, 8 due to the pressure of hydraulic fluid within the cylinders 13, are urged against the cam faces 21, 22 at all times, and make rolling contact therewith.

The cam track 21 has a number of half-lobes such as that indicated at 21a each of which, when traversed by one of the balls 7 is accompanied by an outward (or force) stroke of the ball when table 11 is moving to the left or by an inward (or exhaust) stroke when table 11 is moving to the right, a complete cam lobe is indicated at 211; and a complete cam repeat pattern extending over the distance I: P =m F is indicated at 21c. The half of a complete cam lobe such as 2111, other than the half lobe 21a is accompanied converse motions of the balls passing over it.

The ducts 18 are respectively connected to conduits 25, 26, 27, 28 and 30, 31, 32, 33 (FIG. 4). Conduits 25 and 30, 26 and 31, 27 and 32 and 28 and 33 are connected to common conduits 34, 35, 36 and 37 respectively. The four conduits 34 to 37 communicate with four radial ducts 40, 41, 42 and 43 (FIG. 3) which are respectively provided in a sleeve 44 of a spool valve 45, the spool 46 of which is rotatably mounted therein.

Four flutes formed in the spool 46 provide four channels 50, 51, 52, 53 extending along the length of the spool such that they communicate in turn with the conduits 34 to 37. Channels 50 and 52 communicate via radial ducts 54, 55 with a central bore 56 which itself communicates with a conduit 57 (FIG. 2) provided in housing 12. Channels 51, 53 communicate with longitudinal bores 60 in the spool 46 which in turn communicate with a conduit 61 (FIG. 2) formed in the hous ing 12.

Conduits 57 and 61 communicate via an electrohydraulic valve 62 either with an inlet 63 for hydraulic oil under pressure or with an exhaust (not shown) according to the positioning of the electrohydraulic valve 62. Thus either conduit 57 or 61 can be connected to the inlet 63 or exhaust (not shown) according to the setting of the valve 62 which is under the control of the operator of the machine.

In the position of the spool valve 45 shown in FIGS. 2 and 3 the channels 50 and 52 communicate with the radial ducts 40, 42 and the channels 51, 53 communicate with the radial ducts 41, 43. Thus, assuming valve 62 to be so set that hydraulic fluid is supplied from the inlet 63 to the conduit 57 and that the conduit 61 is connected to the exhaust, hydraulic fluid under pressure will be supplied via the common conduits 34 and 36 to the cylinders containing balls 7a, 8a, 70, 8c, 7e, 8e and 7g, 8g. The cylinders containing the balls 7b, 8b, 7d, 8d, 7f, 8f, and 7):, 8h will be connected to exhaust. The pressure differential on the balls will exert a thrust on the table 11 and thus the table 11 will be caused to move. It will be appreciated that, by using the valve 62 to reverse the connections between the conduits 57, 61 and the inlet 63 and the exhaust (not shown), the direction of movement of the table 11 can be reversed. v

To ensure that the table 11 will continue to move once movement has started due to pressure differences within the eight cylinders, the spool 46 of the spool valve 45 is provided at its left-hand end, as seen in FIG. 2, with a pinion 70 which meshes with a rack 71 fixed to the table 11. Movement of table 11, initiated by using the valve 62, will therefore cause pinion 70 and thus spool 46 to rotate thereby connecting the conduits 34-37 to supply and exhaust in turn and thereby connecting the various cylinders 13 to supply and exhaust in turn. It is so arranged that pressure variations between the cylinders are such as to keep the table 11 moving at a constant predetermined speed once movement has been initiated. The cam profile and the relationship between ramp pitch and spacing between consecutive balls 7 or 8 are such, and the number ol bails is such, that for a constant hydraulic pressure input via inlet 63, a constant force is exerted by the balls 7, 8 upon the cam surfaces 21, 22 thereby to provide the predetermined constant speed required. This is achieved, by arranging that the cam profiles produce in each ball, during a half-cycle of its reciprocation in its cylinder 13, a motion having three consecutive phases namely, a period of constant acceleration, a succeeding period of constant velocity, and a final period of constant deceleration, as described above.

Ne ve refit of the table can be stopped by actuation of the a e It will be appreciated that the use of common cylinders 13 within which two balls 7, 8 are disposed, substantially reduces the amount of space within which hydraulic fluid is to be contained and the number of conduits leading fluid to and from the cylinders is reduced and is in fact halved compared for example with the arrangement shown in U.I(. Pat; specification No. 924,906 or No. 961,339. Also, using the inserts 14 in the cylinders 13 and thereby filling any dead area withinthe cylinders 13 a further reduction in the space required tobe filled by hydraulic fluid is achieved and the arrangement is therefore made yet hydraulically stiffer. The use of a common control valve 45 as opposed to individual control valves for each of the cylinders 13 provides a further saving in conduit space. A particularly stifi' and therefore accurate hydraulic drive is accordingly provided with the present invention. Thus the table may be controlled more accurately and, additionally, the natural frequency of the table and its control gear can be raised thus reducing tool chatter.

The table is moreover directly driven from a location on the bed near the point of application of the tool, and therefore the bed of the machine need only resist the reactive force occurring between the drive and the floor beneath the drive, the remainder of the bed merely serving to support the table.

There is nolirnit iri practice to the length of the table provided it is adequately supported along its length.

The manner in which the acceleration phase of one ball coincides with the deceleration phase of another ball and also the manner in which the dwells are arranged according to the invention is readily seen from FIGS. 5 and 6.

FIG. 5 is the velocity diagram for the embodiment illustrated in FIGS. 1 to 4 and the curves corresponding to the balls designated 7a-7h in FIG. I are for simplicity designated a-h in FIG. 5.

This embodiment has eight balls and two complete lobes in the distance n P, and may be described as an 8/2 arrangement.

With an 8/2 arrangement, the highest common factor L of the ball number n and the lobe number m is 2. The expression n/L=8/2=4, which is an even number. The proportion of the stroke of each ball occupied by the constant velocity phase is therefore equal to the expression l(4L/n=l8l8= zero, so that the constant velocity phase is reduced to zero. However FIG. 5 relates to a cam shape which provides a dwell, as hereinbefore described, and this necessitates the reintroduction of a constant velocity phase to balance the dwell.

In FIG. 5 the vertical axis represents the velocity of a. ball in the course of axial motion along its cylinder and the horizontal axis represents the distance travelled by a ball along the cam track. The diagrams representing the velocities of the eight balls 0, b, e, d, e,f, g and It are superimposed one above the other in the correct time relationship and the solid lines of the graph represent the power stroke of the ball while the dotted lines represent the exhaust stroke.

The manner in which the deceleration phase of one ball is arranged to coincide with the acceleration phase of another ball and the manner in which the dwell of one ball is made to coincide with a part of the constant velocity phase of another ball is shown in the drawing by the phase positions concerned being circled with a small circle and the two coinciding phases are linked together with a chain dotted line. For instance, at the point along the horizontal axis indicated by the arrow 65 the deceleration phase of ball a is seen to coincide with the acceleration phase of ball b and the dwell following the deceleration phase of ball a is seen to coincide with part of the constant velocity of ball 17. This pattern is repeated in respect of balls e and f. In the period represented by arrow 66 it will be seen that the dwell at the beginning of the power stroke of ball c coincides with the last portion of the constant velocity phase of ball [7. The deceleration phase of ball 6 corresponds to the acceleration phase of ball c and the dwell following the deceleration phase of ball b is seen to coincide with the beginning of the constant velocity phase of ball c. This pattern is repeated further up the graph in respect of balls f and Moving onward to the zone indicated by arrow 67 it will be seen that the acceleration phase of ball 11 coincides with the deceleration phase of ball and similar pairings take" place in respect of balls 3 and h. Similarly the dwell following deceleration of ball c coincides with the beginning of the constant velocity phase of ball d. The dwell of ball 3 similarly coincides with the beginning of the constant velocity phase of ball h.

This pattern of pairings is repeated for the remainder of FIG. 5.

Examination of FIG. will show that each power stroke of a hall, indicated by solid lines in FIG. 5, is succeeded by an exactly similar but inverted velocity diagram which represents the exhaust stroke of the ball and cylinder combination in question. Unless the velocity diagrams have this characteristic the drive is not fully reversible because, on reversing, the dotted line exhaust strokes become, the power strokes. It is furthermore necessary that the velocity diagrams should be symmetrical about the midstroke position, that is to say the position in the middle of the constant velocity phase.

FIG. 6 is a similar diagram to FIG. 5, and the same reference numerals are used for corresponding names. FIG. 6 relates to a machine having nine balls A, B, C, D, E, F, G, H and I, and the structure of thisdrive is indicated by a partial section shown in FIG. 7 from which it will be seen that the distance representing the number of balls multiplied by the interball pitch distance accommodates exactly six lobes of the cam track. This may be described as 9/6 arrangement.

The same method of indicating the coincidence of the various mutually balancing phases of the various balls is that used in FIG. 5, is used in FIG. 6. For instance at the point along the horizontal axis indicated by the arrow 65 the deceleration phase of ball A is seen to coincide with the acceleration phase of ball B and the dwell following the deceleration phase of ball A is seen to coincide with part of the constant velocity phase of ball B. This pattern is repeated in respect of balls D and E and balls G and H. In the period represented by arrow 66 it will be seen that the dwell at the beginning of the power stroke of ball C coincides with the last portion of the constant velocity phase of ball B. The deceleration phase of ball B corresponds to the acceleration phase of ball C and the dwell phase following the deceleration phase of ball B is seen to coincide with the beginning of the constant velocity phase of ball C. This pattern is continued up the graph in respect of balls E and F and H and I. Moving onward to the zone indicated by arrow 67 it will be seen that the acceleration phase of ball A coincides with the deceleration phase of ball C and similar pairings take place in respect of ball D and F and G and I. Similarly the dwell following deceleration of ball C coincides the beginning of the constant velocity phase of ball A. The dwEEiidii F similarly coincides with the beginning of the constant velocity phase of ball D and the dwell of ball I similarly corresponds with the beginning of the constant velocity phase of ball G. Turning now to the point indicated by arrow 68 it will be seen that the dwell preceding the accelera tion phase of ball B coincides with the end of the constant velocity phase of ball A and similar pairings take place with respect to balls E and D and balls H and G. Again, as in the case of F IG. 5 each power stroke of '5 ball, indicated by solid lines in FIG. 6, is succeeded by an exactly similar but inverted velocity diagram which represents the exhaust stroke of the ball and cylinder combination in question. Also, the velocity diagrams are symmetrical about the midstroke position, that is to say the position in the middle of the constant velocity phase.

Inset FIG. 6A shows the mannerin whicha velocity diagram where dwell is not provided, has to be modified when dwell is provided. There are two superimposed diagrams, the upper one of which shows the velocity diagram of the power stroke of one ball of a 9/6 arrangement similar to that shown in FIG. 5 and it will be seen that the acceleration phase starts at the point indicated by the arrow 69 and to the left of this point dotted lines indicate the terminal part of the previous exhaust stroke, the acceleration phase of the powerstroke being seen to be a continuous extension of this exhaust stroke. At points indicated by arrow 70, the acceleration phase ceases and the constant velocity phase starts, continuing until point indicated by arrow 71, at which point the deceleration phase commences and continues until the point indicated by the arrow 72, whereafter the exhaust stroke commences and the velocity diagram shows a continuous straight line. It should be realized that the points 69 and 72 represent the points of zero velocity and reversal of direction of the ball. A

Coming now to the lower diagram in FIG. 6A; a dwell 73 has been inserted at the inner dead center position and it will be seen from the dotted lines to the left indicating the terminal parts of the preceding exhaust stroke that a similar dwell occurred at the end of that stroke making in effect two units of dwell at the inner dead center. The beginning of the constant velocity phase is advanced as shown at 74 because this has to balance the dwell at the end of the stroke of another ball forinstance in the case of balls I and H shown vertically below in The end of the constant velocity phase is extended as shown at 75 and this is necessary to balance a dwell on the part of another ball, for instance, the ball G, vertically below in FIG. 6. The succeeding deceleration phase 76 begins later and ends earlier to provide for the dwell 77 at the outer dead center.

It will be noticed that the acceleration and deceleration phases in the two diagrams of FIG. A have their midpoints coinciding but the acceleration and deceleration phases,

where dwell is provided, are steeper.

It is evident from FIG. 5A that the amount of dwell provided can be determined without reference to the basic equations for the lobe and ball combination. For the purpose for which dwell is required, namely to enable the tolerances to be eased on the construction of the control valve, the dwell does not require to be of very long duration and it is possible to choose the amount of dwell provided, solely on these considerations.

Inset FIG. 6B illustrates the modification, previously described, where the periods of acceleration and deceleration begin and finish with nonabrupt transitions.

The upper diagram shows the velocity diagram without dwell. The abrupt transition in passing from negative to positive acceleration is indicated as a slight flattening" of the curve at 78 and 79.

The modification of the acceleration phase at 78 must be matched by a compensating modification at the beginning of the deceleration phase of another ball, as at 80. Similarly the modification of the deceleration phase at 79 must be matched by a compensating modification at the end of the acceleration phase of another ball, as at 81.

Corresponding modifications can be made where dwell is provided as shown in the lower diagram of FIG. 6B. lt mustbestressedfiiatsmoothing de center transitions in this way is not a substitute for a dwell to the extent of enabling tolerances to be relaxed on the valve. It is possible however to cut down the length of dwell provided, when dead center transitions are smoothed since, if a valve passage is not completely opened (or closed as the case may be) at the end of a very short dwell the smoothing of the transition to acceleration or from deceleration minimizes the effect of the uncompleted valve action by delaying the full onset of ball acceleration or the complete cessation of deceleration.

The actual arrangement of a 9/6 machine corresponding to the velocity diagrams in FIG. 6, is shown in FIG. 7 which is to some extent self-explanatory. It will be noticed that the balls are arranged in groups of three in relation to the cam track and three balls A, D, and G can be fed from one port, B, E and M from another port and C, F and I from a third port. The valve 45 is shown diagrammatically in FIG. 7 but is in fact constructed in a manner similar to the valve 45 of FIG. 2 and 3, except that it is provided with three outlets instead of four. The length of the repeating cycle is shown by the dimensional arrow 84 and this is the distance n P,,, which is equal to m P of the equation set out previously.

The six cam lobes 78, 79, 80, 81, 82 and 83 are marked with arrows and the last lobe 83 may be regarded as terminating at point level with the center of an imaginary additional ball shown in dotted lines at A.

We claim:

1. A hydraulic machine including two parts which are relatively movable along an arcuate path of radius up to and including infinity, that is to say including a linear path, one of the parts having a series of cylinders with piston members therein, and the other part having a cam track aligned along the said path and engageable by the piston members, the cylinders and pistons being arrayed side by side along the direction of the cam track and valve means operable to supply fluid to and release fluid from the cylinders in accordance with the relative positions of the parts, the cam track having a series of similarly contoured half-lobes each having a profile which causes a piston member moving thereover, during a half-cycle of its reciprocation in a cylinder, to have three consecutive phases of motion, namely an acceleration phase, a succeeding constant velocity phase and a final deceleration phase and the variations in the velocity of movement of each piston member in its cylinder during the said acceleration and deceleration periods being balanced by oppositely phased and conjugate velocity variations resulting from movement of another piston member in its cylinder over the appropriate sections of a halflobe of the cam track, the constant velocity phase occupying not less than a proportion of the said half-cycle according to the expression l-2L/n) when n/L is an odd number and according to the expression l(4L/n) when n/L is an even number, n being the number of cylinders and L being the highest common factor of n and m is the number of lobes of the cam track spanned by a distance along the said path equal to n times the distance between the axes of adjacent cylinders, including the case where the value of the expression l-4L/n is zero.

2. A hydraulic machine as claimed in claim 1 in which the acceleration and deceleration of a piston member are constant during the acceleration and deceleration phases respectively.

3. A hydraulic machine as claimed in claim 1 in which each piston member presents to the cam track a profile which is at least part of a circle when viewed from a direction normal to the plane of the cam track.

4. A hydraulic machine as claimed in claim 2 in which the profile of each half-lobe is so shaped that the path followed by a point on each piston member during the three consecutive phases of motion is defined by the following three equations, namely:

Constant acceleration phase:

r n 0 2 II r 2(n-1)(H/m) for 0 6 mn Constant velocity phase:

l l1 c:- .E r 2(n-1) II/m n mn n m Constant deceleration phase:

1' n I 0 2 n1 II 77 m'( T in setsm where:

n is a number of pistons and cylinders m is the number of lobes contained within a distance 1: P

measured along the cam track P is the cylinder pitch distance 0 =21rx/mP where x is the distance of the center of the cylinder along the cam track from the bottom dead center of the first lobe and P is the cam lobe pitch distance and-is expressed in radians r is the distance of the center of said circle from its bottom dead center position r is the stroke of the piston in its cylinder These equations applying to the case where either m or n is in odd integer, m and n have no common factor greater than lorto the case where m and n are even integers m/2 and n/2 have no common factor greater than l, and n/2 is greater than 3.

5 A hydraulic machirE as claimed in'claim 1 in which the profile of the cam track is so shaped that each piston member dwells at zero velocity at its innermost position in the cylinder and at its outermost position in the cylinder, any such dwell on the part of one piston coinciding in time with part of the constant velocity phase of another piston.

6. A hydraulic machine as claimed in claim 1 in which each piston member consists of a spherical ball.

7. A hydraulic machine as claimed in claim 1 in which each piston member comprises a spherical ball mounted therein which engages the cam track.

8. A hydraulic machine as claimed in claim 1 in which each piston member comprises a part spherical element engaging the cam track.

9. A hydraulic machine as claimed in claim 1 in which each piston is provided with a cylindrical roller mounted in the end thereof which engages the cam track.

10. A hydraulic machine as claimed in claim 1 comprising a cylinder block having a plurality of transverse bores therein in each end of which there is a piston member so that each such bore constitutes two outwardly facing cylinders whereby there are provided two duplicated banks of cylinders and piston ing the piston members of one of the banks of cyiinders. fluid being introduced to each of the said bores at the middic thereof betweon the two piston members. 

1. A hydraulic machine including two parts which are relatively movable along an arcuate path of radius up to and including infinity, that is to say including a linear path, one of the parts having a series of cylinders with piston members therein, and the other part having a cam track aligned along the said path and engageable by the piston members, the cylinders and pistons being arrayed side by side along the direction of the cam track and valve means operable to supply fluid to and release fluid from the cylinders in accordance with the relative positions of the parts, the cam track having a series of similarly contoured half-lobes each having a profile which causes a piston member moving thereover, during a half-cycle of its reciprocation in a cylinder, to have three consecutive phases of motion, namely an acceleration phase, a succeeding constant velocity phase and a final deceleration phase and the variations in the velocity of movement of each piston member in its cylinder during the said acceleration and deceleration periods being balanced by oppositely phased and conjugate velocity variations resulting from movement of another piston member in its cylinder over the appropriate sections of a half-lobe of the cam track, the constant velocity phase occupying not less than a proportion of the said half-cycle according to the expression 1- 2L/n) when n/L is an odd number and according to the expression 1- (4L/n) when n/L is an even number, n being the number of cylinders and L being the highest common factor of n and m is the number of lobes of the cam track spanned by a distance along the said path equal to n times the distance between the axes of adjacent cylinders, including the case where the value of the expression 1- 4L/n is zero.
 2. A hydraulic machine as claimed in claim 1 in which the acceleration and deceleration of a piston member are constant during the acceleration and deceleration phases respectively.
 3. A hydraulic machine as claimed in claim 1 in which each piston member presents to the cam track a profile which is at least part of a circle when viewed from a direction normal to the plane of the cam track.
 4. A hydraulic machine as claimed in claim 2 in which the profile of each half-lobe is so shaped that the path followed by a point on each piston member during the three consecutive phases of motion is defined by the following three equations, namely:
 5. A hydraulic machine as claimed in claim 1 in whiCh the profile of the cam track is so shaped that each piston member dwells at zero velocity at its innermost position in the cylinder and at its outermost position in the cylinder, any such dwell on the part of one piston coinciding in time with part of the constant velocity phase of another piston.
 6. A hydraulic machine as claimed in claim 1 in which each piston member consists of a spherical ball.
 7. A hydraulic machine as claimed in claim 1 in which each piston member comprises a spherical ball mounted therein which engages the cam track.
 8. A hydraulic machine as claimed in claim 1 in which each piston member comprises a part spherical element engaging the cam track.
 9. A hydraulic machine as claimed in claim 1 in which each piston is provided with a cylindrical roller mounted in the end thereof which engages the cam track.
 10. A hydraulic machine as claimed in claim 1 comprising a cylinder block having a plurality of transverse bores therein in each end of which there is a piston member so that each such bore constitutes two outwardly facing cylinders whereby there are provided two duplicated banks of cylinders and piston members according to claim 1, the machine further comprising two inwardly facing cam tracks, each according to claim 1, and fast with the said other part, each such cam track engaging the piston members of one of the banks of cylinders, fluid being introduced to each of the said bores at the middle thereof between the two piston members. 